Andrew Neitzke

Four-dimensional wall-crossing via three-dimensional field theory

We give a physical explanation of the Kontsevich-Soibelman wall-crossing formula for the BPS spectrum in Seiberg-Witten theories. In the process we give an exact description of the BPS instanton corrections to the hyperkähler metric of the moduli space of the theory on

BPS black holes, quantum attractor flows and automorphic forms

{\mathbb R^3 \times S^1}

Rationality, quasirationality and finite W-algebras

. The wall-crossing formula reduces to the statement that this metric is continuous. Our construction of the metric uses a four-dimensional analogue of the two-dimensional tt* equations.

Spectral Networks and Snakes

A bstractWe introduce a new wall-crossing formula which combines and generalizes the Cecotti-Vafa and Kontsevich-Soibelman formulas for supersymmetric 2d and 4d systems respectively. This 2d-4d wall-crossing formula governs the wall-crossing of BPS states in an

Argyres-Seiberg Duality and the Higgs Branch

\mathcal{N}=2

Quasi-Conformal Actions, Quaternionic Discrete Series and Twistors : SU(2, 1) and G2(2)

supersymmetric 4d gauge theory coupled to a supersymmetric surface defect. When the theory and defect are compactified on a circle, we get a 3d theory with a supersymmetric line operator, corresponding to a hyperholomorphic connection on a vector bundle over a hyperkähler space. The 2d-4d wall-crossing formula can be interpreted as a smoothness condition for this hyperholomorphic connection. We explain how the 2d-4d BPS spectrum can be determined for 4d theories of class

Line Defects, Tropicalization, and Multi-Centered Quiver Quantum Mechanics

\mathcal{S}

Wild Wall Crossing and BPS Giants

, that is, for those theories obtained by compactifying the six-dimensional (0, 2) theory with a partial topological twist on a punctured Riemann surface C. For such theories there are canonical surface defects. We illustrate with several examples in the case of A1 theories of class